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Lecture 22 : Four cosmic puzzles and Inflation

 The cosmic jigsaw  Four puzzles…  How inflation solves

these puzzles

Reading: Chapter 16 of text (inflation)

© Sidney Harris

Reminder #1

 Review session: Tuesday May 10th  Final is Monday May 16th at 10:30am in

this room

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Reminder #2: Course Evaluation  Open through Wednesday, May 11 http://www.CourseEvalUM.umd.edu

 Note: The evaluations are confidential, I will not be able to identify who has submitted an evaluation, only the participation rate.

 Goal is to achieve >70% response rate  We are currently at 45% response rate.

Thanks for participating! 5/4/11 3

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I : THE FLATNESS PROBLEM  Universe with a flat geometry is a very

special case…  Ω = 1 (for standard models)  Ω+Λ = 1 (for models with cosmological constant)

 Our universe is almost flat…  We measure ΩM approximately 0.3  CBR results suggest that ΩM+ΩΛ ≈ 1 to within 1

percent or better!  Why are we so close to this special case?   Also remember that Ω = 1 is a universe with zero

total energy: kinetic and gravitational potential energy (negative sign) balance each other!

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In fact, problem is much worse…

 If Ω ≠ 1, then value changes with cosmic time…  If Ω > 1, then it grows larger and larger  If Ω < 1, then it grows smaller and smaller

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 If the universe is approximately flat now, it had to be very, very flat at early times…  Ω ≈ 1 now means Ω (t = 1s) differed from 1 by

less than 10-16 !!  At the Planck’s time, Ω differed from 1 by less

than 10-60 !!  So, very special conditions were needed in the

early universe to give approximate flatness now.  If the Universe were not nearly flat, we would

not be here…  If Ω had been much above 1, it would have recollapsed

very early before making galaxies  If Ω had been much below 1, it would have expanded so

rapidly that structures would not have formed  This requires a lot of fine tuning!  It is known as the flatness problem

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II : THE HORIZON PROBLEM  Concept of the particle horizon:

 The sphere surrounding a given point (e.g., the Earth) which is causally connected to that point

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  Consider 3 locations in space; A, B and C.   Let’s draw their particle horizons…

  So, in this example, A and B are causally connected to each other. But C is not causally connected to either A or B.

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 Consider the “epoch of recombination”  Occurred ~400,000 yrs after big-bang  At that time, particle horizon would be

roughly 106 light years across.  This size-scale at the redshift of

decoupling (z = 1000) corresponds to an angle of about 1° on the sky…

 So, patches of the CBR that are separated by more than 1 degree should not have been in causal contact at the time of decoupling

 This gives the horizon problem…

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 There were a million causally-disconnected regions on sky at the time of last scattering

 How does the CBR “know” that it has to be so uniform across the sky?!

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III : THE STRUCTURE PROBLEM   Structure in the universe (galaxies, clusters of galaxies

etc.) came from inhomogeneities in the early universe  We see those same inhomogeneities in the CBR maps…

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  How did those inhomogeneities get there?  Why are they just the right magnitude and size to

produce the structures we see today?   How is it possible to have the same kind of

inhomogeneities spread throughout the whole universe, despite the lack of causal contact between different parts of the early universe?   CBR is statistically the same in all directions  Galaxies, etc., that formed are similar in properties, on

opposite sides of the Universe

  This is the structure problem.

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IV : THE RELIC PROBLEM   Analogy: consider the cooling of a liquid (e.g.,

water)  Once liquid reaches freezing point…

  Freezing does not occur smoothly and uniformly   Freezing starts at certain locations, and the crystals start

growing.  When crystals eventually merge to form the solid, there

will be dislocations where the individual crystals meet…   The process of freezing is called a “phase

transition” (matter changing from one phase to another).

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Dislocations in steel

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Beer crystals (Bud)...

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 What does this have to do with the Universe?   “Quantum fields” related to particles and forces in

the very early universe can undergo phase transitions (i.e., they “freeze”).

  As Universe cools…   The temperature falls to the point where certain phase

transitions can occur   Phase transitions will start at particular points in space and

grow at light speed   Can get “dislocations” produced in the universe as a result

of different regions meeting

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  This would produce exotic structure called topological defects…   Domain walls (2-d sheet-like structures)   Cosmic Strings (1-d string-like structures)   None of these structures have been seen in the observable

universe (good limits from CBR data – strings would gravitationally lens the background)

 GUTs predict exotic particles produced at these domain walls in the early Univese   Look like magnetic monopoles   Never yet detected… and they don’t reveal their presence

in any observed phenomena. Limits are very good. These objects have to be very very very rare.

  The absence of monopoles (and other relics predicted by particle physics theories) is called the relic problem

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I.BASIC IDEA OF INFLATION

 Theory of cosmic “inflation” was first proposed by Alan Guth in 1982

 Guth postulated an Inflationary Epoch  Very-rapid, exponential expansion of Universe  Occurs during interval t=10-37-10-32 s  Universe expanded by a factor of 1040-10100

during this time!

 What caused inflation? We’ll get to that later…

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II : SOLVING “COSMOLOGICAL PROBLEMS” WITH INFLATION

  The Flatness Problem   Imagine taking any (reasonable) curved

surface   Now expand it by an enormous factor   After the expansion, locally it will look flat   So, inflation predicts a Universe that is

indistinguishable from being flat

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 The Horizon Problem  Prior to inflation (at t ≈ 10-37 s), the particle horizon

has radius of r ≈ 10-29 m  A sphere of this radius is the maximum volume that

is causally connected at t ≈ 10-37 s (i.e. in which there can be a mutual influence)

 After inflation (at t ≈ 10-32 s), this region has exploded to 1011 – 1070 m

 “Normal” expansion then takes over… Universe expands by another factor of 1022 between end of inflation and recombination/decoupling (t = 400,000 yr)

 So, at time of decoupling, causally connected volumes have radii at least rc =1033 m!

 This is much larger than today’s particle horizon: r~13.7 billion light years ~1026 m

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 The structure problem  The initial inhomogeneities are due to quantum

fluctuations during the inflationary epoch.  Virtual particle pairs that formed would be

separated by inflationary expansion before they could annihilate, creating uneven densities

 Inhomogeneities were continually created, and then stretched to much larger scales -- outside the horizon

 Naturally gives a characteristic spectrum of inhomogeneities  This is the “Harrison-Zel’dovich spectrum”  Equal amplitude for fluctuations on all scales  Equivalent to “white noise” in acoustics: “static”

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 Relic problem  Suppose exotic particles or structures

(cosmic strings, magnetic monopoles etc.) were created in very early universe

 They would become very diluted during the inflationary epoch, because space would expand so much

 The probability that we see a “relic” exotic particle in our current universe would then be very, very small.

 Inflation solves the relic problem!

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Baryons

 But what about baryons? Wouldn’t the probability of finding them also be small?

 No, provided that baryogenesis occurred after inflation stopped: vacuum energy is converted to regular matter (including baryons) and radiation

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 OK… inflation can solve many “cosmic problems”

 But why did inflation happen?

 We believe the answer lies in the behavior of quantum fields.

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Fields and particles  Quantum view of EM radiation:

  Basic entity is the electromagnetic field (which permeates all of space)

  Photons are excitations (ripples) of field with certain wavelengths and frequencies

  Energy/momentum of the excitations in the field is quantized… can only add or take away energy/momentum from field in discrete amounts equaling the energy in a single photon

  Every particle has its own field   Electron Field (excitations = electrons)  Quark Fields (excitations = quarks)  Gluon Fields (excitations = gluons)   etc. etc.

  Position and momentum of a particle cannot both be known simultaneously, but obey certain probabilistic rules related to the field’s wave behavior

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IV: FALSE VACUUMS AND VARIOUS INFLATION MODELS

 Alan Guth’s original idea…   In early universe, there was an exotic particle (called

“inflaton”) and a corresponding scalar quantum field   As the very early universe evolved, this field got stuck in a

high-energy state  Analogous to a marble resting on top of an upside-down

bowl, or a pencil balanced vertically on its point   This created an enormous “false vacuum” energy that

drove the inflation of the Universe.   Similar to “dark energy” which is making the Universe

expand now!   Eventually, field gets “unstuck” and evolves to a lower-

energy state corresponding to “true vacuum”, so that inflation ends.

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 Guth originally thought the Higgs Boson (a massive particle related to baryogenesis) would work as the “inflaton”

 Guth’s original model turned out not to work because inflation would not stop

 “New” inflation or Chaotic inflation  Proposed independently by Linde and Steinhardt  Inflation occurs during slow rolling of field down

a potential. The field is non-zero initially due to quantum or thermal fluctuations

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Old inflation, produced by a phase transition

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New Inflation: chaotic inflation

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Universe starts simple but becomes very complex!

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 Final philosophical remarks: •  Universe evolves form order (low entropy)

to disorder (high entropy), but in special places in the universe order wins

•  Life and intelligent life around stars is possible because radiation from the sun is used and degraded to higher entropy thermal radiation

•  A brain is certainly a very low entropy system (in most people)

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THE END I hope you enjoyed the course!

Thanks!